From 82e6cf7d1046d6cee16f7e8b044ec33e7ec6c4b7 Mon Sep 17 00:00:00 2001 From: Nguyễn Gia Phong Date: Sun, 16 Feb 2020 14:26:55 +0700 Subject: [usth] Numerical Method is MATH2.4 --- usth/MATH2.2/labwork/2/report.tex | 88 --------------------------------------- 1 file changed, 88 deletions(-) delete mode 100644 usth/MATH2.2/labwork/2/report.tex (limited to 'usth/MATH2.2/labwork/2/report.tex') diff --git a/usth/MATH2.2/labwork/2/report.tex b/usth/MATH2.2/labwork/2/report.tex deleted file mode 100644 index c4481fa..0000000 --- a/usth/MATH2.2/labwork/2/report.tex +++ /dev/null @@ -1,88 +0,0 @@ -\documentclass[a4paper,12pt]{article} -\usepackage[english,vietnamese]{babel} -\usepackage{amsmath} -\usepackage{lmodern} -\usepackage{hyperref} -\usepackage{tikz} - -\newcommand{\exercise}[1]{\noindent\textbf{#1.}} -\renewcommand{\thesection}{\Roman{section}} -\renewcommand*{\thefootnote}{\fnsymbol{footnote}} - -\title{Numerical Method: Labwork 2 Report} -\author{Nguyễn Gia Phong--BI9-184} -\date{Fall 2019} - -\begin{document} -\maketitle -\setcounter{section}{2} -\section{Polynomial} -\exercise{1.c} At the time of writing, function \verb|fzero| -in Octave have not support the \verb|Display| option -just yet\footnote{Bug report: \url{https://savannah.gnu.org/bugs/?56954}}. -However, the implementation of this option is rather trivial, -thus I made a quick patch (which is also attached at the bug report). -Using this, one can easily display all the iterations as followed: - -\begin{verbatim} -octave:1> fzero (@(x) x.^2 - 9, 0, optimset ('display', 'iter')) - -Search for an interval around 0 containing a sign change: -Func-eval 1, how = initial, a = 0, f(a) = -9, b = 0, f(b) = -9 -Func-eval 2, how = search, a = 0, f(a) = -9, b = 0.099, f(b) = -8.9902 -Func-eval 3, how = search, a = 0, f(a) = -9, b = 0.1025, f(b) = -8.98949 -Func-eval 4, how = search, a = 0, f(a) = -9, b = 0.095, f(b) = -8.99098 -Func-eval 5, how = search, a = 0, f(a) = -9, b = 0.11, f(b) = -8.9879 -Func-eval 6, how = search, a = 0, f(a) = -9, b = 0.075, f(b) = -8.99437 -Func-eval 7, how = search, a = 0, f(a) = -9, b = 0.15, f(b) = -8.9775 -Func-eval 8, how = search, a = 0, f(a) = -9, b = 0, f(b) = -9 -Func-eval 9, how = search, a = 0, f(a) = -9, b = 0.35, f(b) = -8.8775 -Func-eval 10, how = search, a = 0, f(a) = -9, b = -0.4, f(b) = -8.84 -Func-eval 11, how = search, a = 0, f(a) = -9, b = 1.1, f(b) = -7.79 -Func-eval 12, how = search, a = 0, f(a) = -9, b = -4.9, f(b) = 15.01 - -Search for a a zero in the interval [-4.9, 0]: -Func-eval 13, how = initial, x = 0, f(x) = -9 -Func-eval 14, how = interpolation, x = -1.83673, f(x) = -5.62641 (NaN%) -Func-eval 15, how = interpolation, x = -3.36837, f(x) = 2.3459 (141.7%) -Func-eval 16, how = interpolation, x = -3.19097, f(x) = 1.1823 (-49.6%) -Func-eval 17, how = interpolation, x = -2.99725, f(x) = -0.0164972 (-101.4%) -Func-eval 18, how = interpolation, x = -3.00258, f(x) = 0.0154927 (193.9%) -Func-eval 19, how = interpolation, x = -3, f(x) = 3.07975e-07 (-100.0%) -Func-eval 20, how = interpolation, x = -3, f(x) = -7.10543e-15 (-100.0%) -Func-eval 21, how = interpolation, x = -3, f(x) = 5.32907e-15 (169.7%) - -Algorithm converged - -ans = -3.0000 -\end{verbatim} - -To answer the question in part b, (since I believe these parts are linked -to each other), the current implementation of \verb|fzero| search for -the second bracket over quantitative chages below if \verb|X0| if it is a -single scalar, thus $[-4.9, 0]$ is gotten and the found solution is negative: - -\begin{verbatim} -[-.01 +.025 -.05 +.10 -.25 +.50 -1 +2.5 -5 +10 -50 +100 -500 +1000] -\end{verbatim} - -\section{Non-linear Systems} -\exercise{1.a} These statements were used to plot the given functions: -\begin{verbatim} -ezplot(@(x1, x2) x1 .^ 2 + x1 .* x2 - 10) -hold on -ezplot(@(x1, x2) x2 + 3 .* x1 .* x2 .^ 2 - 57) -\end{verbatim} - -As shown in the graphs (where $x_1^2 + x_1 x_2 = 10$ are the blue lines -and $x_2 + 3 x_1 x_2 = 57$ are the yellow ones), the solutions of $(x_1, x_2)$ -are quite close to $(2, 3)$ and $(4.5, -2)$. - -\begin{figure}[!h] - \centering - \scalebox{0.37}{\input{2a.tikz}} -\end{figure} - -I would also like to note that I am personally impressed how gnuplot -(which is utilised by Octave) is able to export to TikZ graphics with ease. -\end{document} -- cgit 1.4.1